H Chamati and N S Tonchev 2006 J. Phys. A: Math. Gen. 39 469 doi:10.1088/0305-4470/39/3/001
H Chamati and N S Tonchev
Show affiliationsThe difficulties arising in the investigation of finite-size scaling in d-dimensional O(n) systems with strong anisotropy and/or long-range interaction, decaying with the interparticle distance r as r−d−σ(0 < σ ≤ 2), are discussed. Some integral representations aiming at the simplification of the investigations are presented for the classical and quantum lattice sums that take place in the theory. Special attention is paid to a more general form allowing to treat both cases on an equal footing and in addition cases with strong anisotropic interactions and different geometries. The analysis is simplified further by expressing this general form in terms of a generalization of the Mittag–Leffler special functions. This turned out to be very useful for the extraction of asymptotic finite-size behaviours of the thermodynamic functions.
05.70.Ce Thermodynamic functions and equations of state
05.70.Fh Phase transitions: general studies
Issue 3 (20 January 2006)
Received 12 August 2005, in final form 22 November 2005
Published 21 December 2005
H Chamati and N S Tonchev 2006 J. Phys. A: Math. Gen. 39 469
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